FastReg: Fast Non-Rigid Registration via Accelerated Optimisation on the Manifold of Diffeomorphisms

We present a new approach to diffeomorphic non-rigid registration of medical images. The method is based on optical flow and warps images via gradient flow with the standard $L^2$ inner product. To compute the transformation, we rely on accelerated optimisation on the manifold of diffeomorphisms. We achieve regularity properties of Sobolev gradient flows, which are expensive to compute, owing to a novel method of averaging the gradients in time rather than space. We successfully register brain MRI and challenging abdominal CT scans at speeds orders of magnitude faster than previous approaches. We make our code available in a public repository: https://github.com/dgrzech/fastreg